Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm
Introduction
Over the past few decades, stereo image processing technology has drawn attention to increasingly more research. Stereo images are based on binocular parallax of the human eye to obtain three-dimensional sense. The existence of binocular parallax makes the human brain perceive the depth of the information in an image and gives people a strong visual shock and a sense of being immersed [3]. However, stereo images are easy to copy and modify, which seriously infringes upon the copyright of the author. Therefore, the copyright protection for stereo images is a serious problem to be solved.
As is known, image watermarking technology is the main technology that is used to protect the copyright of planar images [28]. However, research on stereo image digital watermarking technology has only recently started. Based on the adaptive disparity matching algorithm and DCT, Lee et al. [13] proposed a novel stereo image watermarking algorithm for copyright protection, which improves the PSNR value of the extracted watermark image from the reconstructed image. Yu et al. [32] put forward a new stereo image watermarking algorithm that is based on block-relationships. This algorithm applies the intra-block and inter-block relationships for embedding watermarks. A semi-fragile digital watermarking algorithm based on the discrete wavelet transform (DWT) domain of the stereo image left and right views was presented by Campisi [4]. This algorithm is robust to JPEG2000 compression, but it is fragile to other malicious attacks. Based on fractional Fourier transform (FrFT) and singular value decomposition (SVD), Bhatnagar et al. [2] brought forward a robust stereo image watermarking algorithm, which has strong robustness and security. Lin et al. [17] designed a blind depth-image-based rendering (DIBR) 3D image watermarking algorithm, which has good robustness to some common image processing attacks. A more robust DIBR 3D image watermarking algorithm based on dual-tree complex wavelet transform (DT-CWT) was presented by Kim et al. [12], which achieves good imperceptibility. Wang et al. [27] proposed a watermarking algorithm for DIBR 3D images based on SIFT feature points, which is robust to some common image processing attacks. Cui et al. [8] presented a robust blind DIBR 3D images watermarking algorithm, which achieves good robustness to geometric attacks and common image processing attacks. Zhou et al. [33] proposed a novel binocular visual characteristics-based pixel-wise fragile watermarking algorithm, which is used for stereoscopic image authentication and locating tampered regions. Al-Haj et al. [1] came up with a 3D DIBR image watermarking algorithm based on the hybrid DWT and SVD transforms; the algorithm has good imperceptibility and robustness.
In addition, since the zero-watermarking algorithm [30] can provide good balance between the robustness and the imperceptibility, it has become one of the research hotspots in digital watermarking technology. Since zero-watermarking technology was proposed, many scholars have conducted in-depth research and proposed many excellent algorithms. The concept of zero-watermarking technology was proposed by Wen et al. [30]. These authors indicate that the zero-watermarking technology focuses on how to construct watermark information using image features rather than on how to embed watermark information into image features. Chen et al. [7] proposed a zero-watermarking system for public copyright authentication. That algorithm constructs a feature matrix from the low-frequency coefficients of the original image wavelet domain and uses it as a watermark matrix. This algorithm can effectively resist the interpretation attack and makes up for the shortcomings of the traditional zero-watermarking system. Chang and Lin [5] improved the feature extraction method on the basis of the algorithm in [7] and proposed a new zero-watermarking algorithm in the spatial domain. This scheme uses Sobel edge detection to extract the feature matrix. Gao and Jiang [10] designed and developed a robust visual zero-watermarking scheme based on Bessel-Fourier moments. The zero-watermark image is constructed using the magnitudes of the Bessel-Fourier moments. Chen et al. [6] proposed a zero-watermarking method for stereo images based on the texture features of the image block. First, the one-level DWT transform is performed on the left and right views of the stereo image, and the approximate coefficients of the DWT transform are calculated; then, the approximate coefficients are divided into non-overlap blocks and classified according to the texture of the block; finally, the block type relationship between the blocks is used to construct the zero-watermark information. Zhou et al. [34] proposed a zero-watermarking algorithm for stereo image copyright protection by studying the disparity stability of the DWT domain of the stereo image left and right views and the pseudo randomness of the hyperchaotic discrete system, which has good robustness to all types of symmetric and asymmetric attacks. Wang et al. [26] proposed a geometric attack-resistant color image zero-watermarking algorithm based on quaternion exponential moments (QEMs). Experimental results indicate that the proposed algorithm resists various attacks significantly better than similar zero-watermarking algorithms and the QEMs-based traditional watermarking algorithm. Later, they developed a new zero-watermarking algorithm [24] using logistic mapping and polar complex exponential transform (PCET). Logistic mapping is used to randomly select PCET coefficients in this algorithm, which can improve the security of the algorithm.
In summary, researchers have conducted some research on stereo image traditional watermarking technology and planar image zero-watermarking technology. However, there is little research on stereo image zero-watermarking algorithms. Moreover, most of them do not consider the intrinsic relationship between the left and right views of a stereo image, which lowers the performance of the zero-watermarking algorithm. In addition, they can only resist common image processing attacks and cannot resist geometric attacks effectively, such as rotation and scaling. To solve the above problems, based on ternary number theory and radial harmonic Fourier moments (RHFM), ternary radial harmonic Fourier moments (TRHFM) is proposed here, and based on this moment, the present paper proposes a robust stereo image zero-watermarking algorithm. In this algorithm, TRHFM effectively deals with stereo images in a holistic manner, which preserves the special relationship between the left and right views. At the same time, TRHFM has good geometric invariance, which will effectively improve its capability in resisting geometric attacks. The TRHFM of the original stereo image is computed first, and the robust moments suitable for constructing a zero-watermark are selected. Then, a binary feature image is constructed by using the magnitudes of the selected robust moments. Finally, a bitwise exclusive-or operation between the binary feature image and the permuted binary logo image is performed to generate the zero-watermark image. Experiment results show that the proposed algorithm can effectively resist common image processing attacks and geometric attacks and show the superiority of the proposed algorithm compared with other zero-watermarking algorithms.
The remainder of this paper is organized as follows. Section 2 introduces the definition and properties of TRHFM. Section 3 presents the proposed stereo image zero-watermarking algorithm. Experimental analysis and results are discussed in Section 4. Finally, Section 5 concludes the paper.
Section snippets
Radial harmonic Fourier moments
The definition of the radial harmonic Fourier moments (RHFM) [22] is as follows: where ϕnm is the RHFM of order n(n ≥ 0) with repetition m(|m| ≥ 0), and Tn(r) is the radial basis function (RBF), which is defined as follows:
The basic function is orthogonal in the unit circle: where 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, is the
Zero-watermark generation
By using ternary number theory, the stereo image can be treated as a vector field, and the zero-watermark image can be constructed directly using the TRHFM magnitudes. As is known, the exclusive-or operation satisfies the following rule:
Hence, the exclusive-or operation is used for the zero-watermark generation procedure and zero-watermark verification procedure, which can achieve the blind watermark verification.
Let be the original grayscale
Experimental results
Twenty grayscale stereo images from Middlebury 2005 Stereo Datasets [23] with 512 × 512 pixels and one binary logo image with 64 × 64 pixels are used to investigate the performance of the proposed algorithm. The left and right views of the four grayscale stereo images ‘Art’, ‘Books’, ‘Computer’ and ‘Dolls’ and the binary logo image are shown in Fig. 4. The max moment order of TRHFM is set to .
Conclusions
This paper proposes ternary radial harmonic Fourier moments (TRHFM) for stereo images based on ternary number theory and radial harmonic Fourier moments (RHFM). Based on TRHFM, we propose a robust stereo image zero-watermarking algorithm, which implements copyright protection for stereo images. Experimental results show that the proposed algorithm is strongly robust to various asymmetric and symmetric attacks and has better performance compared with other zero-watermarking algorithms. The
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos: 61802212, 61872203, 61502241, 61672124, 61370145 and 61173183), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund(No: MMJJ20170203), A Project of Shandong Province Higher Educational Science and Technology Program (J18KA331).
Chunpeng Wang received the B.E. degree in computer science and technology in 2010 from Shandong Jiaotong University, China, the M.S. degree from the School of Computer and Information Technology, Liaoning Normal University, China, 2013, and the Ph.D. degree in Faculty of Electronic Information & Electrical Engineering, Dalian University of Technology, China, 2017. He is currently a teacher with the School of Information, Qilu University of Technology (Shandong Academy of Sciences), China. His
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Chunpeng Wang received the B.E. degree in computer science and technology in 2010 from Shandong Jiaotong University, China, the M.S. degree from the School of Computer and Information Technology, Liaoning Normal University, China, 2013, and the Ph.D. degree in Faculty of Electronic Information & Electrical Engineering, Dalian University of Technology, China, 2017. He is currently a teacher with the School of Information, Qilu University of Technology (Shandong Academy of Sciences), China. His research mainly includes image watermarking and signal processing.
Xingyuan Wang received the PhD degree in computer software and theory from Northeast University, China, 1999. From 1999 to 2001, he was a postdoctoral researcher at Northeast University. He is currently a professor with the Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, China. He has published five books and more than 420 scientific papers in refereed journals and proceedings. His research interests include nonlinear dynamics and control, image processing, chaos cryptography, systems biology, and complex networks.
Zhiqiu Xia received the M.S. degree from the School of Computer Science, University of Leicester, UK. She is currently pursuing the PhD degree in Faculty of Electronic Information & Electrical Engineering, Dalian University of Technology, China. Her research mainly includes image processing and systems biology.
Chuan Zhang received the B.S. degree in Statistics from Qufu Normal University, China, in 2013. From 2013 to 2015, he was a master at Nanjing University of Finance and Economics. He is currently working toward the PhD degree with the Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, China. His research interests include systems biology and complex networks.